Structural Risk Minimization for Nonparametric Time Series Prediction

The problem of time series prediction is studied within the uniform convergence frameworkof Vapnik and Chervonenkis. The dependence inherent in the temporal structure is incorporated into the analysis, thereby generalizing the available theory for memoryless processes. Finite sample boundsare calculated in terms of covering numbers of the approximating class,and the tradeoff between approximation and estimation is discussed. A complexity regularization approach is outlined, based on Vapnik's method of Structural Risk Minimization, and shown to be applicable inthe context of mixing stochastic processes.